Stability analysis remains a key focus in the nonlinear field. The stability of oscillator networks considering phase-lag coupling is still an unsolved puzzle. Here, we investigate the linear stability using the maximal Lyapunov exponent and evaluate the basin stability by numerical simulations. The results show that the phase lag has no significant effect on the proportion of twisted states with linear stability and on their basin sizes, without considering higher-order interactions. In contrast to the stabilizing effect of higher-order interactions on twisted states, pairwise coupling suppresses their linear stability but enhances their basin stability. When pairwise coupling dominates, phase lag acts to strengthen the linear stability of the twisted state. Furthermore, the phase lag reduces the degree of ordering of the system and shrinks the basin of the twisted state. These results highlight the synergistic effect of phase lag with pairwise and higher-order interactions on twisted-state basins.

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• Chimera states
• Dynamics of networks
• Synchronization
• Coupled oscillators